Describe strong boundary points for Au(Bℓp) and identify fibers containing them

Describe all strong boundary points of the algebra Au(Bℓp) for 1 ≤ p < ∞, and, at minimum, identify all fibers in the maximal ideal space M(Au(Bℓp)) that contain strong boundary points.

Background

Strong boundary points play a fundamental role in uniform algebras, and for Au(Bℓp) they are tied to the geometry of the underlying Banach space and the structure of fibers. For uniformly convex spaces (including ℓp with 1 < p < ∞), evaluations at points on the sphere are known peak points and hence strong boundary points, but a global classification across all p and all fibers is lacking.

The authors pose a general problem to systematize which homomorphisms are strong boundary points in Au(Bℓp), and to determine which fibers contain them, motivated by examples and partial results throughout the paper.